Subgroups — C₃×#453 #5327

Order 192.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
3	C₃×#127	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#104	C₂	1	2	yes	maximal, complemented
5	C₃×#100	C₂	1	1	yes	maximal, characteristic, complemented
6	#453	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₃×#41	—	2	2	no	—
8	C₃×#41	C₂²	1	2	yes	—
9	C₂×C₃×D₄	—	2	2	no	—
10	C₂×C₃×D₄	—	2	2	no	—
11	C₂×C₃×D₄	—	2	2	no	—
12	C₂×C₃×D₄	C₂²	1	1	yes	characteristic
13	C₂×C₃×D₄	C₂²	1	1	yes	characteristic, complemented
14	C₃×SD₁₆	—	2	2	no	—
15	C₃×D₈	—	2	2	no	—
16	C₃×M₁₆	C₂²	1	2	yes	complemented
17	C₃×C₄²	C₂²	1	1	yes	characteristic, complemented
18	H(5,𝔽₂)	C₂×C₃	1	1	yes	characteristic, complemented
19	AGL(1,ℤ/8)	C₂×C₃	1	2	yes	complemented
20	#127	C₂×C₃	1	1	yes	characteristic, complemented
21	#104	C₂×C₃	1	2	yes	complemented
22	#100	C₂×C₃	1	1	yes	characteristic, complemented
23	C₂³×C₃	—	2	2	no	—
24	C₂³×C₃	—	2	1	no	—
25	C₂³×C₃	D₄	1	2	yes	—
26	C₃×Q₈	D₄	1	2	yes	complemented
27	C₃×D₄	—	2	4	no	—
28	C₃×D₄	—	2	2	no	—
29	C₃×D₄	—	2	2	no	—
30	C₃×D₄	—	2	2	no	—
31	C₃×D₄	—	4	4	no	—
32	C₃×D₄	D₄	1	2	yes	complemented
33	C₂×C₃×C₄	—	2	2	no	—
34	C₂×C₃×C₄	—	2	1	no	—
35	C₂×C₃×C₄	—	2	2	no	—
36	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
37	C₃×C₈	—	2	2	no	—
38	#41	—	2	2	no	—
39	#41	C₂²×C₃	1	2	yes	—
40	C₂×D₄	—	2	2	no	—
41	C₂×D₄	—	2	2	no	—
42	C₂×D₄	—	2	2	no	—
43	C₂×D₄	C₂²×C₃	1	1	yes	characteristic
44	C₂×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
45	SD₁₆	—	2	2	no	—
46	D₈	—	2	2	no	—
47	M₁₆	C₂²×C₃	1	2	yes	complemented
48	C₄²	C₂²×C₃	1	1	yes	characteristic, complemented
49	C₂²×C₃	—	2	2	no	—
50	C₂²×C₃	—	2	2	no	—
51	C₂²×C₃	—	4	2	no	—
52	C₂²×C₃	—	4	2	no	—
53	C₂²×C₃	—	4	1	no	—
54	C₂²×C₃	—	8	2	no	—
55	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
56	C₃×C₄	—	2	2	no	—
57	C₃×C₄	—	2	2	no	—
58	C₃×C₄	C₂×D₄	1	2	yes	—
59	C₂³	—	2	2	no	—
60	C₂³	—	2	1	no	—
61	C₂³	C₃×D₄	1	2	yes	—
62	Q₈	C₃×D₄	1	2	yes	complemented
63	D₄	—	2	4	no	—
64	D₄	—	2	2	no	—
65	D₄	—	2	2	no	—
66	D₄	—	2	2	no	—
67	D₄	—	4	4	no	—
68	D₄	C₃×D₄	1	2	yes	complemented
69	C₂×C₄	—	2	2	no	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	2	2	no	—
72	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
73	C₈	—	2	2	no	—
74	C₂×C₃	—	2	1	no	—
75	C₂×C₃	—	4	2	no	—
76	C₂×C₃	—	4	2	no	—
77	C₂×C₃	—	8	1	no	—
78	C₂×C₃	#120	1	1	yes	characteristic
79	C₂²	—	2	2	no	—
80	C₂²	—	2	2	no	—
81	C₂²	—	4	2	no	—
82	C₂²	—	4	2	no	—
83	C₂²	—	4	1	no	—
84	C₂²	—	8	2	no	—
85	C₂²	C₂×C₃×D₄	1	1	yes	characteristic
86	C₄	—	2	2	no	—
87	C₄	—	2	2	no	—
88	C₄	C₂×C₃×D₄	1	2	yes	—
89	C₃	#453	1	1	yes	characteristic, direct product factor, Sylow
90	C₂	—	2	1	no	—
91	C₂	—	4	2	no	—
92	C₂	—	4	2	no	—
93	C₂	—	8	1	no	—
94	C₂	C₃×#120	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃	#120
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃×H(5,𝔽₂)	C₂	semidirect
2. C₃×AGL(1,ℤ/8)	C₂	semidirect
3. C₃×#127	C₂	semidirect
4. C₃×#104	C₂	semidirect
5. C₃×#100	C₂	semidirect
6. #453	C₃	direct (N × H)
13. C₂×C₃×D₄	C₂²	semidirect
16. C₃×M₁₆	C₂²	semidirect
17. C₃×C₄²	C₂²	semidirect
18. H(5,𝔽₂)	C₂×C₃	semidirect
19. AGL(1,ℤ/8)	C₂×C₃	semidirect
20. #127	C₂×C₃	semidirect
21. #104	C₂×C₃	semidirect
22. #100	C₂×C₃	semidirect
26. C₃×Q₈	D₄	semidirect
32. C₃×D₄	D₄	semidirect
44. C₂×D₄	C₂²×C₃	semidirect
47. M₁₆	C₂²×C₃	semidirect
48. C₄²	C₂²×C₃	semidirect
62. Q₈	C₃×D₄	semidirect
68. D₄	C₃×D₄	semidirect
89. C₃	#453	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×H(5,𝔽₂)	2
C₃×AGL(1,ℤ/8)	2
C₃×#127	2
C₃×#104	2
C₃×#100	2
#453	3

Subgroups — C3×#453 #5327

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#453 #5327